Three charges, Q 1 , Q 2 , and Q 3 are located in a straight line. The position

Question

Three charges, Q1, Q2, and Q3 are located in a straight line. The position of Q2 is 0.257 m to the right of Q1. Q3 is located 0.180 m to the right of Q2. The force on Q2 due to its interaction with Q3 is directed to the.....
True False - Right if the two charges are negative.
True False - Left if the two charges are positive.
True False - Left if the two charges have opposite signs.
True False - Right if the two charges have opposite signs.
True False - Left if the two charges are negative.

In the above problem, Q1= 1.56·10-6 C, Q2= -2.84·10-6 C, and Q3= 3.03·10-6 C. Calculate the total force on Q2. Give with the plus sign for a force directed to the right.

Now the charges Q1= 1.56·10-6 C and Q2= -2.84·10-6 C are fixed at their positions, distance 0.257 m apart, and the charge Q3= 3.03·10-6 C is moved along the straight line. For what position of Q3 relative to Q1 is the net force on Q3 due to Q1 and Q2 zero? Use the plus sign for Q3 to the right of Q1.

Explanation / Answer

Q2 is in between Q1 and Q3.

Q1 is at leftside of Q2 and Q3 is at rightside of Q2.

if two charge are negative. then Q3 will repel Q2 to the left.

False

if two charge are positive. then Q3 will repel Q2 to the left.

True

if two charge are of opposite sign then Q3 will attract Q2 to the right.

False

if two charge are of opposite sign then Q3 will attract Q2 to the right.

True

if two charge are negative. then Q3 will repel Q2 to the left.

True

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Q1 will attract leftward.

F1= - kq1q2/d^2 = - (9 x 10^9) (1.56 x 10^-6)(2.84 x 10^-6) / 0.257^2

F1 = - 0.604 N

Q3 will attract to the rightside.

F3 = (9 x 10^9) (3.03 x 10^-6)(2.84 x 10^-6) / 0.180^2

F3 = 2.39 N

F2 = F1 + F3 = 1.786 N

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force on q3 will be zero for position at distance d from Q1 (to the left)

Fnet = - [ k(1.56uC) (3.03uC) / d^2 ] + [ k (2.84uC) (3.03 uC) / (d + 0.257)^2] = 0

1.56 / d^2 = 2.84 / (d^2 + 0.514d + 0.066)

1.56 d^2 +0.802d + 0.103 = 2.84d^2

1.28 d^2 - 0.802 d - 0.103 = 0

d = 0.736 m

Q3 is to the left of Q1.

hence d = - 0.736 m

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